DeBrincat has scored eight goals during an NHL career-high six-game goal streak and 10 points (eight goals, two assists) during a seven-game point streak.
"A lot of times I'm not getting that last one or even that first one, but you know I'll take them," DeBrincat said. "Sometimes they're just finding the back of the net and sometimes they don't. I just got to keep improving all of the other areas of my game as well."
Brandon Hagel had a goal and an assist, and Kevin Lankinen made 37 saves for the Blackhawks (24-25-6), who have won two straight after going 0-5-1 in their previous six games.
Denis Gurianov and Mark Pysyk scored, and Anton Khudobin made 21 saves for the Stars (22-19-14).
Chicago and Dallas have been eliminated from contention for the Stanley Cup Playoffs. The Stars were eliminated Saturday when the Nashville Predators clinched the fourth and final playoff berth from the eight-team Discover Central Division; the Carolina Hurricanes, Florida Panthers and Tampa Bay Lightning have the other postseason berths.
"Our guys were a very down group this morning, to wake up and know you're out of the [playoffs] after everything we've been through," Dallas coach Rick Bowness said. "I could tell there wasn't a lot of energy in the room in the meeting this morning because of that. They're all really down that we're out. So you start the game like that, you're down 3-1, then we fought back … We had a really good second period, and we had enough scoring chances to get back in the game. [Lankinen] made some big saves and they get that fourth goal and the game's over."